Your brother has offered to give you $$185,$ starting next year, and after that growing at $2\mathrm{.}9\%$ per year for the next $20$ years. You would like to calculate the value of this offer by calculating how much money you would need to deposit in a local bank so that the amount will generate the same cash flows as he is offering you. Your

local bank will guarantee a $6\mathrm{.}3\%$ annual interest rate so long as you have money in the account.

a$.$ How much money will you need to deposit into the account today?

b$.$ Assuming you deposited the amount of money in part $($a$),$ and then withdrew the required payments each year, calculate the remaining balance at the end of years $1,2,10$ and $19.($Hint$.$ To solve this problem it is best to use an excel spreadsheet.$)$